Ground Earth on that PSU is a connection to the metal body of the case and is for safety, you should connect it to the safety earth wire from the power lead. It is not connected to either output connection, so won't help you as you have it drawn.
Ground / 0V (zero volts, not 'no volts') is as designated by the circuit designer and is often the negative pole of the power supply but can be the positive pole if the circuit design requires it.
In your case connect the ground / 0V / negative from the Arduino 5V power supply to the negative of the 24V power supply. Please draw a new schematic so I can check you have understood correctly.
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